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ChatGPT
Aug 10
To find the domain and range of the function f(x) = 2/√(x-3), we need to consider the restrictions on the input values (x) and the possible output values (y).
Domain:
The function f(x) = 2/√(x-3) is defined for all real numbers except when the denominator becomes zero. In this case, the denominator becomes zero when x - 3 = 0, which means x = 3. Therefore, the domain of the function is all real numbers except x = 3. In interval notation, the domain is (-∞, 3) U (3, ∞).
Range:
To find the range of the function, we need to consider the possible values that the function can take. Since the function involves a square root, the output values (y) will always be positive. Additionally, as x approaches 3 from the right, the function approaches positive infinity. Therefore, the range of the function is (0, ∞).
Domain:
The function f(x) = 2/√(x-3) is defined for all real numbers except when the denominator becomes zero. In this case, the denominator becomes zero when x - 3 = 0, which means x = 3. Therefore, the domain of the function is all real numbers except x = 3. In interval notation, the domain is (-∞, 3) U (3, ∞).
Range:
To find the range of the function, we need to consider the possible values that the function can take. Since the function involves a square root, the output values (y) will always be positive. Additionally, as x approaches 3 from the right, the function approaches positive infinity. Therefore, the range of the function is (0, ∞).
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Google Gemini AI
Aug 10
The domain of the function is the set of all values of x for which the function is defined. The range of the function is the set of all values of y that the function can take on.
For the function f(x) = 2/root x-3, the domain is all values of x such that x-3 > 0. This is because the square root of a negative number is not a real number. Therefore, the domain is x > 3.
The range of the function is all values of y such that y = 2/root x-3. Since the square root of a number is always non-negative, the range is y > 0.
For the function f(x) = 2/root x-3, the domain is all values of x such that x-3 > 0. This is because the square root of a negative number is not a real number. Therefore, the domain is x > 3.
The range of the function is all values of y such that y = 2/root x-3. Since the square root of a number is always non-negative, the range is y > 0.
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Aug 10
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